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ME
1( SZ
Circle in a Mathematical Point; which has no Parts or
Dimenfions, confequently no Magnitude: but a Thing that
hais no Magnitude or Dimenfions, bears no proportion to
another that has; and cannot therefore meafure it. Hence
we fee the Reafon of the Divifion of Circles into 360
Parts or Arches, called Degrees. See DEGREE.
. MEASURING of Triangles, or from threegiven Sides or
Angles, to determine all the reft, is call'd Trigonometry.
See TRIGONOMETRY.
MEASVRIXN    of the Sir; its Prefure, Spring, Eec. is
Called Aerometry or Pneumatics: See AEROMETRY,  c.
MEATUS Cyfticus, a Bilary Dudt, about the Bignefs
of a Goofe-Quill, which at about two Inches diflance from
the Gall-Bladder, is join'd to the Meatus Repaticus ; and
thefe together form the DuZEus Communis. See BILE.
MEATUS Lrinarins, or Urinary .Pafage, in Women, is
very lhort, lined internally with a very thin Membrane i
next to which is a Coat of a white Subttance. Thro this
Coat, from fome Lacxne in it, pafs feveral Dudfs, which
convey a limpid glutinous Matter, ferving to anoint the
Extremity of the Lrrethra. See URINARY.
MPATVS Auditorins, the Entrance of the Ear; a carti-
laginous Subfiance, irregularly divided with flelhy mem-
branous Interpofitions in feveral Parts of it, not unlike the
Bronchia in the Lungs, only its flethy Fibres are here
thicker. The inner Part, or that next the Brain, is bony.
It is lined throughout with a thin Membrane, derived
from the Skin, which is continued on the Membrana T~ym-
pani, where it becomes thinner. See EaR.
From the beginning of the Meatus, almofi half-way, a-
rife a great number of fmall Hairs, at whofe Roots iffue
the Ear-Wax, which is intangled in thofe Hairs, the bet-
ter to break the Impetus of the external Air, and prevent
its too fuddenly rufhing in on the Memkrana Tympani. See
CEFUM EN.
MECHANICS, from usvAs', Engine, is a mix'd Ma-
thematical Science, which confiders Motion, its Nature and
Laws, with the Effefs thereof, in Machines, Lec. See
MOTION.
That part of Mechanics which confiders the Motion of
Bodies arifing from Gravity, is by fome call'd Statics.
See GtAViTY, StAtICS, RESIS TENce, Wc. In diffinaion
from that part which confiders the Mechanic Powers, and
their Application, properly call'd Mechanics. See ME-
CNANIC POWERS, MA:IuNE, ENGINE, FRICTION, EQ.VILI-
311PM, kec.
MECHANIC POters, arethe five fimpleMachines; to
which all others, how complex foever, are reducible, and
of the Aifemblage whereof they are all compounded.
See PowER and MACHINE.
Thefe Mecbanic Powers (as they are call'd) are fix, viz.
the hallance, Lever, Wkeel, Puflt, Wedge, and Screw; which
fee under their proper Heads: BALL AN CE, LEVER, ES5C.
They may, however, be all reduced to one, viz. the
Lever. The Principle whereon they depend, is the fame
in all, and may be conceived from what follows.
The Momentum, Impetus, or Quantity of Motion of any
Body, is the Fagum of its Velocity, (or the Space it moves
in a given Time, fee MOTION) multi plied into its Mafs.
Hence it follows, that two unequal Bodies will have equal
Moments, if the Lines they defcribe be in a reciprocal
Ratio of their Maifes. Thus, if two Bodies, faflen'd to the
Extremities of a Ballance or Lever, be in a reciprocal
Ratio of their Diflances from the fixed Point; when they
move, the Lines they defcribe will be in a reciprocal Ra-
tio of their Mlafes. A. -. If the Body A (Tab. MECH A-
NICS, fig'6.) be triple the Body B, and each of them be
fo fix'd to the Extremities of a Lever AB, whofe Ful-
crum, or fix'd Point, is C, as that the fliflance of BC be
triple the Diflance CA ; the Lever cannot be inclined on
either fide: but that the Space BE, pafs'd over by the
lefs Body, will be triple the Space AD, pAYs'd over by
the great one. So that their Motions or Moments will be
equal, and the two Bodies in Equilibrio. See MOTION.
Hence that noble Challenge of Archimedes, datis Viriihus, da-
tum Pandus movere; for as the Diflance C B may be in-
creafed infinitely, the Power or Moment of A may be in-
creafed infinitely. So that the whole of Mechanics is re-
duced to the fillowing Problem.
Any bodly, as A, with its Velocity C, and alfo any other Body,
as B, leings given; to find the Velocity necenary to make the
Moment, or QPantit of Motion in B, equal to the Moment of
A, the given Body. Since, now the Moment of any Body is
equal to the Redangle under the Velocity, and the Quan-
tity of Matter; as B: A:: C: to a fourth Term, which
will be c, the Celerity proper to B, to make its Moment
equal to that of A. Wherefore in any Machine or Engine,
if the Velocity of the Power be made to the Velocity of
the Weight: reciprocally as the Weight is to the Power;
then fball the Power always fuffain, or if the Power be a
little incrcas'd, move the Weight.
)
MEC
Let, for inflance, A B be a Lever, whofe Fulcrum is at C,
and let it be moved into the Pofition a cb. Here the Velo-
city of any Point in the Lever, is as the Diflance from the
Centre. For let the Point A defcribe the Arch A a, and the
Point B the Arch B b i then thefe Arches will be the Spa-
ces defcribed by the two Motions: but fince the Motions
are both made in the fame time, the Spaces will be as the
Velocities. But it is plain, the Arches A a and B b will
be to one another, as their Radii A C and A B, becaufe
the Seiffors A Ca, and Bcb, are fimilar: wherefore the
Velocities of the Points A and B, are as their Difrances from
the Centre C. Now if any Powers are applied to the Ends
of the Lever A and B, in order to raife its Arms up and
down; their Force will be expounded by the Perpendi-
culars S a, and b N; which being as the right Sines of the
former Arches, b B and a A, will be to one another alfo
as the Radii Ac, and c B; wherefore the Velocities of
the Powers, are alfo as their Diflances from the Centre.
And fince the Moment of any Body is as its Weight, or
gravitating Force, and its Velocity conjunrily; if diffe-
rent Powers or Weights are applied to the Lever, their
Moments will always; be as the Weights and their
Diflances from  the Centre conjundly.  Wherefore if
to the fame Lever, there be two Powers or Weights ap-
ply'd reciprocally, proportional to their Didtances from
the Centre, their Moments will be equal; and if they adt
contrarily, as in the Cafe of a Stilliard, the Lever will
remain in an horizontal Pofation, or the Ballance will
be in Equilibrio. And thus it is eafy to conceive how the
Weight of one Pound may be made to equi ballance a
thoufand, tc. Hence alfo it is plain, that the Force of
the Power is not at all increafed by Engines; only the Ve-
locity of the Weight in either lifting or drawing, is fo di-
minilh'd by the Application of the Inilrument, as that the
Moment of the Weight is not greater than the Force of
the Power. Thus, for inflance;j if any Force can elevate
a Pound Weight with a given Velocity, it is impoflible by
any Engine to elFed, that the fame Power [hall raife two
Pound Weight, with the fame Velocity: But by an En.
gine it may be made to raife two Pound Weight, with half
the Velocity; or ioooo times the Weight with  Ad; of
the former Velocity. See PERPETUAL MOTION.
MECHANICAL Curve, a Term ufed by Des Caries for
thofe Curves, which cannot be defined by any Equation ;
in oppofition to Algebraic, which they call Geometric
Curves. Thefe Curves, Sir V.. ANewton, M. Leibnitz, &c.
call tranfcendent Curves; and diffent from Cartes, in ex-
cluding them out of Geometry. Leibnitz has even found
a new kind of tranfcendent Equations, whereby thefe
Curves are defined: They are of an indefinite nature;
that is, don't continue conflantly the fame in all Points of
the Curve; in oppofition to Algebraic Equations, which do.
See CURVE.
MECHANICAL Affeffions, are fuch Properties in Matter,
as refult from their Figure, Bulk, and Motion: MECHA-
NIC AL Catere are thofe founded on fuch Affections; and
MECHANICAL Solutions are Accounts of Things on the
fame Principles.
MECHANICAL 1hilofopby, is the lame with the Corpuf.
cular Philofophy; viz. that which explains the Effeds of
Nature, and the Operations of Corporeal Things, on the
Principles of Mechanics ; the Figure, Arrangement, Difpo-
fition, Motion, Greatnefs or Smallnefs of the Parts which
compofe natural Bodies. See CORPUSCULAR.
The Term MECHANICAL is alfo applied to a kind of
Reafoning, which of late has got a great deal of ground
both in Phyfics and Medicine; fo call'd, as being conform-
able to what is ufed in the Contrivance, and accounting for
the Properties and Operations of Machines. This feems
to have been the Refult of rightly fludying the Powers of
a human Mind, and the Ways by which it is only fitted
to get acquaintance with material Beings: For confider-
ing an Animal Body as a Compofition out of the fame
Matter, from which all other material Beings are formed,
and to have all thofe Properties, which concern a Phy-
lician's Regard qnly, by virtue of its peculiar Make and
Confirudure; it naturally leads a Perfon, who trufls to
pro  Evidences, to confider the feveral Parts, according
to ther Figures, Contexture, and Ufe i either as Wheels,
Pullies, Wedges, Levers, Skrews, Chords, Canals, Ci-
flerns, Strainers, and the like; and throughout the whole
of fuch Enquiries, to keep the Mind cofoe in view of the
Figures, Magnitudes, and mechanical Powers of every Part
or Movement ; jufc in the fame manner, as is ufed, to en-
quire into the Motions and Properties of any other Ma-
chine. For which purpofe it is frequently found helpful
to decypher, or picgure out in Diagrams, whatfoever is
under confideration, as it is cuflomary in common Geo-
metrrial Demonfirations; and the Knowledge obtained by
this Pocedure, is called Mechanical Knowledge.
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